# 31. Change of Basis; Image Compression | Summary and Q&A

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September 24, 2019
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MIT OpenCourseWare
31. Change of Basis; Image Compression

## TL;DR

This lecture discusses the application of linear algebra in image compression, specifically focusing on the use of change of basis and matrix transformations to compress images and videos.

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### Q: What is the main purpose of image compression?

Image compression is used to reduce the amount of data required to store or transmit images, allowing for more efficient storage and faster transmission.

### Q: How is change of basis used in image compression?

Change of basis is used in image compression to exploit redundancies and correlations among pixel values, allowing for more efficient representation of images by using a different set of basis vectors.

### Q: What is the difference between lossless and lossy compression?

Lossless compression retains all the original information of the image, while lossy compression discards some information that is less noticeable to the human eye in order to achieve a higher compression ratio.

### Q: Can you explain the role of the Fourier basis in image compression?

The Fourier basis is commonly used in image compression because it can efficiently represent smooth changes in images, such as gradients and color variations. It allows for the removal of high-frequency noise or details that are less perceptible to the viewer.

## Summary & Key Takeaways

• The lecture introduces the concept of image compression and its importance in reducing the amount of data needed to transmit images and videos.

• The use of change of basis is explained as a method to compress signals, such as images, by exploiting redundancies and correlations among pixel values.

• The lecture also discusses the connection between linear transformations and matrices, and how different basis can result in similar matrices representing the same transformation.